CIF: Small: Collaborative Research: Rank Aggregation with Heterogeneous Information Sources: Efficient Algorithms and Fundamental Limits

虽然收集和存储数据的能力的进步已经使大型数据集变得司空见惯，但这些数据集越来越多地由从不同来源获得的具有各种数据类型和属性的信息组成，这些数据类型和属性阻碍了提取知识和做出决策的能力。该项目的重点是从具有任意噪声的异构数据集中推断一组对象的排名，这也被称为异构信息源的排名聚合。开发的算法将作为开源软件工具公开提供，并将显着扩大排名聚合的适用性，以现实世界的问题，如数据融合，信息检索，众包，推荐系统，以及社会选择和投票。该项目还将提供教育和培训机会，接触先进的统计工具、严格的理论分析以及从大型异质数据集提取知识的经验工作。在本项目中，基于数据的统计模型，将在三个互补的研究方向中，沿着开发适用于各种设置的高效和可扩展的等级聚合算法，并提供性能保证和基本限制。首先，它将开发基于灵活的潜在概率模型的等级聚合算法，该模型利用边信息并允许序数和数值数据类型。它还将提供信息理论上的这种算法的性能的下限。其次，它将为潜在的概率模型设计鲁棒算法，其中未知参数是许多结构化参数的叠加，以及数据可能被任意噪声破坏的模型。最后，将研究通过交互式强盗算法推断排名的问题。该项目旨在推动秩聚合研究的前沿，并有可能推动机器学习、非凸优化和信息理论的研究。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

While advances in the ability to collect and store data have made large data sets commonplace, these data sets increasingly consist of information obtained from different sources with various data types and properties that impede the ability to extract knowledge and make decisions. This project focuses on inferring the ranking of a set of objects from heterogeneous datasets with arbitrary noise, which is also known as rank aggregation with heterogeneous information sources. The developed algorithms will be made publicly available as open source software tools, and will significantly expand the applicability of rank aggregation to real-world problems, such as data fusion, information retrieval, crowd-sourcing, recommendation systems, as well as social choice and voting. This project will also provide educational and training opportunities and exposure to sophisticated statistical tools, rigorous theoretical analysis, and the empirical work of extracting knowledge from large heterogeneous data sets. In this project, based on statistical models of data, efficient and scalable rank aggregation algorithms for various settings will be developed along with performance guarantees and fundamental limits, in three complementary research thrusts. First, it will develop rank aggregation algorithms based on flexible latent probabilistic models that exploit side information and allow both ordinal and numerical data types. It will also provide information-theoretic lower bounds on the performance of such algorithms. Second, it will design robust algorithms for latent probabilistic models in which the unknown parameters are a superposition of many structured parameters, and models in which data can be corrupted by arbitrary noise. Finally, the problem of inferring a ranking through interactive bandit algorithms will be studied. This project aims to push the frontier of rank aggregation research, and can potentially advance research in machine learning, nonconvex optimization and information theory.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.